Place the chicken, 8 ounces Island Salsa (or use your favorite mango-pineapple salsa), lime juice, olive oil, and black pepper in a large ziptop bag, seal, and turn the bag until the chicken is evenly coated, then refrigerate for at least 30 minutes. The chicken should look fully slicked with marinade, and longer marinating will deepen the fruit and lime flavor.
Oil the grill grates lightly and heat the grill to medium-high. A properly heated grill should give the chicken a satisfying sizzle right away, which helps prevent sticking and builds good char.
Put the sliced yellow bell pepper in a grill basket, drizzle with the 2 tablespoons olive oil, season with kosher salt and black pepper, and toss to coat. The peppers should look evenly glossy so they soften and blister instead of drying out.
Set the chicken on one side of the grill and the grill basket on the other side, then discard the marinade bag. Close the lid and let the chicken cook for about 4 to 5 minutes on the first side while the edges turn opaque.
Flip the chicken and continue grilling for about 4 to 5 minutes more with the lid closed, stirring the peppers from time to time as they cook. The peppers may finish a little sooner, and the chicken is ready when it is cooked through with opaque flesh and clear juices when pierced.
Transfer the chicken to a serving platter, spoon the remaining 4 ounces Island Salsa (or as desired) over the top, then add the diced mango, pineapple tidbits, and fresh cilantro if using. Let the chicken rest briefly so the juices settle, then serve while everything still smells smoky and bright.